package org.matheclipse.core.integrate.rubi45;


import static org.matheclipse.core.expression.F.*;
import static org.matheclipse.core.integrate.rubi45.UtilityFunctionCtors.*;
import static org.matheclipse.core.integrate.rubi45.UtilityFunctions.*;
import org.matheclipse.core.interfaces.IAST;

/** 
 * IndefiniteIntegrationRules from the <a href="http://www.apmaths.uwo.ca/~arich/">Rubi -
 * rule-based integrator</a>.
 *  
 */
public class IntRules34 { 
  public static IAST RULES = List( 
ISetDelayed(Int(Times(Power(F_,Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_)))),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Integrate(Times(Power(Plus(d,Times(e,x)),m),Power(FSymbol,Plus(a,Times(b,x),Times(c,Sqr(x))))),x),FreeQ(List(FSymbol,a,b,c,d,e,m),x))),
ISetDelayed(Int(Times(Power(F_,v_),Power(u_,m_DEFAULT)),x_Symbol),
    Condition(Int(Times(Power(ExpandToSum(u,x),m),Power(FSymbol,ExpandToSum(v,x))),x),And(And(And(FreeQ(List(FSymbol,m),x),LinearQ(u,x)),QuadraticQ(v,x)),Not(And(LinearMatchQ(u,x),QuadraticMatchQ(v,x)))))),
ISetDelayed(Int(Times(Power(x_,m_DEFAULT),Power(Plus(a_,Times(b_DEFAULT,Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),n_)),x_Symbol),
    Condition(Int(ExpandIntegrand(Times(Power(x,m),Power(Plus(a,Times(b,Power(FSymbol,Times(e,Plus(c,Times(d,x)))))),n)),x),x),And(FreeQ(List(FSymbol,a,b,c,d,e,m),x),PositiveIntegerQ(n)))),
ISetDelayed(Int(Times(Power(Plus(a_,Times(b_DEFAULT,Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),-1),Power(Plus(f_DEFAULT,Times(g_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(Power(Plus(f,Times(g,x)),Plus(m,C1)),Power(Times(a,g,Plus(m,C1)),-1)),Times(CN1,b,Power(a,-1),Int(Times(Power(Plus(f,Times(g,x)),m),Power(FSymbol,Times(e,Plus(c,Times(d,x)))),Power(Plus(a,Times(b,Power(FSymbol,Times(e,Plus(c,Times(d,x)))))),-1)),x))),And(And(FreeQ(List(FSymbol,a,b,c,d,e,f,g),x),RationalQ(m)),Greater(m,C0)))),
ISetDelayed(Int(Times(Power(Plus(a_,Times(b_DEFAULT,Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),n_),Power(Plus(f_DEFAULT,Times(g_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Module(List(Set(u,Block(List(Set($s("§showsteps"),False),Set($s("§stepcounter"),Null)),Int(Power(Plus(a,Times(b,Power(FSymbol,Times(e,Plus(c,Times(d,x)))))),n),x)))),Plus(Dist(Power(Plus(f,Times(g,x)),m),u,x),Times(CN1,g,m,Int(Times(Power(Plus(f,Times(g,x)),Plus(m,Negate(C1))),u),x)))),And(And(And(FreeQ(List(FSymbol,a,b,c,d,e,f,g),x),RationalQ(m,n)),Greater(m,C0)),Less(n,CN1)))),
ISetDelayed(Int(Times(Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_)))),Power(Plus(a_,Times(b_DEFAULT,Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),-1),Power(Plus(f_DEFAULT,Times(g_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(Power(Plus(f,Times(g,x)),m),Log(Plus(C1,Times(b,Power(FSymbol,Times(e,Plus(c,Times(d,x)))),Power(a,-1)))),Power(Times(b,d,e,Log(FSymbol)),-1)),Times(CN1,g,m,Power(Times(b,d,e,Log(FSymbol)),-1),Int(Times(Power(Plus(f,Times(g,x)),Plus(m,Negate(C1))),Log(Plus(C1,Times(b,Power(a,-1),Power(FSymbol,Times(e,Plus(c,Times(d,x)))))))),x))),And(And(FreeQ(List(FSymbol,a,b,c,d,e,f,g),x),RationalQ(m)),GreaterEqual(m,C1)))),
ISetDelayed(Int(Times(Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_)))),Power(Plus(a_DEFAULT,Times(b_DEFAULT,Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),p_DEFAULT),Power(Plus(f_DEFAULT,Times(g_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(Power(Plus(f,Times(g,x)),m),Power(Plus(a,Times(b,Power(FSymbol,Times(e,Plus(c,Times(d,x)))))),Plus(p,C1)),Power(Times(b,d,e,Plus(p,C1),Log(FSymbol)),-1)),Times(CN1,g,m,Power(Times(b,d,e,Plus(p,C1),Log(FSymbol)),-1),Int(Times(Power(Plus(f,Times(g,x)),Plus(m,Negate(C1))),Power(Plus(a,Times(b,Power(FSymbol,Times(e,Plus(c,Times(d,x)))))),Plus(p,C1))),x))),And(FreeQ(List(FSymbol,a,b,c,d,e,f,g,m,p),x),NonzeroQ(Plus(p,C1))))),
ISetDelayed(Int(Times(Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_)))),Power(x_,m_DEFAULT),Power(Plus(a_DEFAULT,Times(b_DEFAULT,Power(F_,v_))),n_)),x_Symbol),
    Condition(Module(List(Set(u,Block(List(Set($s("§showsteps"),False),Set($s("§stepcounter"),Null)),Int(Times(Power(FSymbol,Times(e,Plus(c,Times(d,x)))),Power(Plus(a,Times(b,Power(FSymbol,v))),n)),x)))),Plus(Dist(Power(x,m),u,x),Times(CN1,m,Int(Times(Power(x,Plus(m,Negate(C1))),u),x)))),And(And(And(And(FreeQ(List(FSymbol,a,b,c,d,e),x),ZeroQ(Plus(Times(C2,e,Plus(c,Times(d,x))),Negate(v)))),RationalQ(m)),Greater(m,C0)),NegativeIntegerQ(n)))),
ISetDelayed(Int(Times(Power(G_,Times(h_DEFAULT,Plus(f_DEFAULT,Times(g_DEFAULT,x_)))),Power(Plus(a_,Times(b_DEFAULT,Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),n_DEFAULT)),x_Symbol),
    Condition(Module(List(Set(m,FullSimplify(Times(g,h,Log(GSymbol),Power(Times(d,e,Log(FSymbol)),-1))))),Condition(Times(Denominator(m),Power(GSymbol,Plus(Times(f,h),Times(CN1,c,g,h,Power(d,-1)))),Power(Times(d,e,Log(FSymbol)),-1),Subst(Int(Times(Power(x,Plus(Numerator(m),Negate(C1))),Power(Plus(a,Times(b,Power(x,Denominator(m)))),n)),x),x,Power(FSymbol,Times(e,Plus(c,Times(d,x)),Power(Denominator(m),-1))))),And(RationalQ(m),GreaterEqual(Abs(m),C1)))),FreeQ(List(FSymbol,GSymbol,a,b,c,d,e,f,g,h,n),x))),
ISetDelayed(Int(Times(Power(G_,Times(h_DEFAULT,Plus(f_DEFAULT,Times(g_DEFAULT,x_)))),Power(Plus(a_,Times(b_DEFAULT,Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),n_DEFAULT)),x_Symbol),
    Condition(Module(List(Set(m,FullSimplify(Times(d,e,Log(FSymbol),Power(Times(g,h,Log(GSymbol)),-1))))),Condition(Times(Denominator(m),Power(Times(g,h,Log(GSymbol)),-1),Subst(Int(Times(Power(x,Plus(Denominator(m),Negate(C1))),Power(Plus(a,Times(b,Power(FSymbol,Plus(Times(c,e),Times(CN1,d,e,f,Power(g,-1)))),Power(x,Numerator(m)))),n)),x),x,Power(GSymbol,Times(h,Plus(f,Times(g,x)),Power(Denominator(m),-1))))),And(RationalQ(m),Greater(Abs(m),C1)))),FreeQ(List(FSymbol,GSymbol,a,b,c,d,e,f,g,h,n),x))),
ISetDelayed(Int(Times(Power(G_,Times(h_DEFAULT,Plus(f_DEFAULT,Times(g_DEFAULT,x_)))),Power(Plus(a_,Times(b_DEFAULT,Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),n_DEFAULT)),x_Symbol),
    Condition(Int(Expand(Times(Power(GSymbol,Times(h,Plus(f,Times(g,x)))),Power(Plus(a,Times(b,Power(FSymbol,Times(e,Plus(c,Times(d,x)))))),n)),x),x),And(And(FreeQ(List(FSymbol,GSymbol,a,b,c,d,e,f,g,h),x),Not(RationalQ(FullSimplify(Times(g,h,Log(GSymbol),Power(Times(d,e,Log(FSymbol)),-1)))))),PositiveIntegerQ(n)))),
ISetDelayed(Int(Times(Power(G_,Times(h_DEFAULT,Plus(f_DEFAULT,Times(g_DEFAULT,x_)))),Power(Plus(a_,Times(b_DEFAULT,Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),n_)),x_Symbol),
    Condition(Times(Power(a,n),Power(GSymbol,Times(h,Plus(f,Times(g,x)))),Power(Times(g,h,Log(GSymbol)),-1),Hypergeometric2F1(Negate(n),Times(g,h,Log(GSymbol),Power(Times(d,e,Log(FSymbol)),-1)),Plus(Times(g,h,Log(GSymbol),Power(Times(d,e,Log(FSymbol)),-1)),C1),Simplify(Times(CN1,b,Power(a,-1),Power(FSymbol,Times(e,Plus(c,Times(d,x)))))))),And(And(FreeQ(List(FSymbol,GSymbol,a,b,c,d,e,f,g,h),x),Not(RationalQ(FullSimplify(Times(g,h,Log(GSymbol),Power(Times(d,e,Log(FSymbol)),-1)))))),NegativeIntegerQ(n)))),
ISetDelayed(Int(Times(Power(G_,Times(h_DEFAULT,Plus(f_DEFAULT,Times(g_DEFAULT,x_)))),Power(Plus(a_,Times(b_DEFAULT,Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),n_)),x_Symbol),
    Condition(Times(Power(GSymbol,Times(h,Plus(f,Times(g,x)))),Power(Plus(a,Times(b,Power(FSymbol,Times(e,Plus(c,Times(d,x)))))),Plus(n,C1)),Power(Times(a,g,h,Log(GSymbol)),-1),Hypergeometric2F1(C1,Plus(n,Times(g,h,Log(GSymbol),Power(Times(d,e,Log(FSymbol)),-1)),C1),Plus(Times(g,h,Log(GSymbol),Power(Times(d,e,Log(FSymbol)),-1)),C1),Times(CN1,b,Power(FSymbol,Times(e,Plus(c,Times(d,x)))),Power(a,-1)))),And(And(FreeQ(List(FSymbol,GSymbol,a,b,c,d,e,f,g,h,n),x),Not(RationalQ(FullSimplify(Times(g,h,Log(GSymbol),Power(Times(d,e,Log(FSymbol)),-1)))))),Not(IntegerQ(n))))),
ISetDelayed(Int(Times(Power(G_,Times(h_DEFAULT,u_)),Power(Plus(a_,Times(b_DEFAULT,Power(F_,Times(e_DEFAULT,v_)))),n_)),x_Symbol),
    Condition(Int(Times(Power(GSymbol,Times(h,ExpandToSum(u,x))),Power(Plus(a,Times(b,Power(FSymbol,Times(e,ExpandToSum(v,x))))),n)),x),And(And(FreeQ(List(FSymbol,GSymbol,a,b,e,h,n),x),LinearQ(List(u,v),x)),Not(LinearMatchQ(List(u,v),x))))),
ISetDelayed(Int(Times(Power(G_,Times(h_DEFAULT,Plus(f_DEFAULT,Times(g_DEFAULT,x_)))),Power($p("H"),Times(t_DEFAULT,Plus(r_DEFAULT,Times(s_DEFAULT,x_)))),Power(Plus(a_,Times(b_DEFAULT,Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),n_DEFAULT)),x_Symbol),
    Condition(Module(List(Set(m,FullSimplify(Times(Plus(Times(g,h,Log(GSymbol)),Times(s,t,Log($s("H")))),Power(Times(d,e,Log(FSymbol)),-1))))),Condition(Times(Denominator(m),Power(GSymbol,Plus(Times(f,h),Times(CN1,c,g,h,Power(d,-1)))),Power($s("H"),Plus(Times(r,t),Times(CN1,c,s,t,Power(d,-1)))),Power(Times(d,e,Log(FSymbol)),-1),Subst(Int(Times(Power(x,Plus(Numerator(m),Negate(C1))),Power(Plus(a,Times(b,Power(x,Denominator(m)))),n)),x),x,Power(FSymbol,Times(e,Plus(c,Times(d,x)),Power(Denominator(m),-1))))),RationalQ(m))),FreeQ(List(FSymbol,GSymbol,$s("H"),a,b,c,d,e,f,g,h,r,s,t,n),x))),
ISetDelayed(Int(Times(Power(G_,Times(h_DEFAULT,Plus(f_DEFAULT,Times(g_DEFAULT,x_)))),Power($p("H"),Times(t_DEFAULT,Plus(r_DEFAULT,Times(s_DEFAULT,x_)))),Power(Plus(a_,Times(b_DEFAULT,Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),n_DEFAULT)),x_Symbol),
    Condition(Times(Power(GSymbol,Times(Plus(f,Times(CN1,c,g,Power(d,-1))),h)),Int(Times(Power($s("H"),Times(t,Plus(r,Times(s,x)))),Power(Plus(b,Times(a,Power(FSymbol,Times(CN1,e,Plus(c,Times(d,x)))))),n)),x)),And(And(FreeQ(List(FSymbol,GSymbol,$s("H"),a,b,c,d,e,f,g,h,r,s,t),x),ZeroQ(Plus(Times(d,e,n,Log(FSymbol)),Times(g,h,Log(GSymbol))))),IntegerQ(n)))),
ISetDelayed(Int(Times(Power(G_,Times(h_DEFAULT,Plus(f_DEFAULT,Times(g_DEFAULT,x_)))),Power($p("H"),Times(t_DEFAULT,Plus(r_DEFAULT,Times(s_DEFAULT,x_)))),Power(Plus(a_,Times(b_DEFAULT,Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),n_DEFAULT)),x_Symbol),
    Condition(Int(Expand(Times(Power(GSymbol,Times(h,Plus(f,Times(g,x)))),Power($s("H"),Times(t,Plus(r,Times(s,x)))),Power(Plus(a,Times(b,Power(FSymbol,Times(e,Plus(c,Times(d,x)))))),n)),x),x),And(And(FreeQ(List(FSymbol,GSymbol,$s("H"),a,b,c,d,e,f,g,h,r,s,t),x),Not(RationalQ(FullSimplify(Times(Plus(Times(g,h,Log(GSymbol)),Times(s,t,Log($s("H")))),Power(Times(d,e,Log(FSymbol)),-1)))))),PositiveIntegerQ(n)))),
ISetDelayed(Int(Times(Power(G_,Times(h_DEFAULT,Plus(f_DEFAULT,Times(g_DEFAULT,x_)))),Power($p("H"),Times(t_DEFAULT,Plus(r_DEFAULT,Times(s_DEFAULT,x_)))),Power(Plus(a_,Times(b_DEFAULT,Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),n_)),x_Symbol),
    Condition(Times(Power(a,n),Power(GSymbol,Times(h,Plus(f,Times(g,x)))),Power($s("H"),Times(t,Plus(r,Times(s,x)))),Power(Plus(Times(g,h,Log(GSymbol)),Times(s,t,Log($s("H")))),-1),Hypergeometric2F1(Negate(n),Times(Plus(Times(g,h,Log(GSymbol)),Times(s,t,Log($s("H")))),Power(Times(d,e,Log(FSymbol)),-1)),Plus(Times(Plus(Times(g,h,Log(GSymbol)),Times(s,t,Log($s("H")))),Power(Times(d,e,Log(FSymbol)),-1)),C1),Simplify(Times(CN1,b,Power(a,-1),Power(FSymbol,Times(e,Plus(c,Times(d,x)))))))),And(And(FreeQ(List(FSymbol,GSymbol,$s("H"),a,b,c,d,e,f,g,h,r,s,t),x),Not(RationalQ(FullSimplify(Times(Plus(Times(g,h,Log(GSymbol)),Times(s,t,Log($s("H")))),Power(Times(d,e,Log(FSymbol)),-1)))))),NegativeIntegerQ(n)))),
ISetDelayed(Int(Times(Power(G_,Times(h_DEFAULT,Plus(f_DEFAULT,Times(g_DEFAULT,x_)))),Power($p("H"),Times(t_DEFAULT,Plus(r_DEFAULT,Times(s_DEFAULT,x_)))),Power(Plus(a_,Times(b_DEFAULT,Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),n_)),x_Symbol),
    Condition(Times(Power(GSymbol,Times(h,Plus(f,Times(g,x)))),Power($s("H"),Times(t,Plus(r,Times(s,x)))),Power(Plus(a,Times(b,Power(FSymbol,Times(e,Plus(c,Times(d,x)))))),n),Power(Times(Plus(Times(g,h,Log(GSymbol)),Times(s,t,Log($s("H")))),Power(Times(Plus(a,Times(b,Power(FSymbol,Times(e,Plus(c,Times(d,x)))))),Power(a,-1)),n)),-1),Hypergeometric2F1(Negate(n),Times(Plus(Times(g,h,Log(GSymbol)),Times(s,t,Log($s("H")))),Power(Times(d,e,Log(FSymbol)),-1)),Plus(Times(Plus(Times(g,h,Log(GSymbol)),Times(s,t,Log($s("H")))),Power(Times(d,e,Log(FSymbol)),-1)),C1),Simplify(Times(CN1,b,Power(a,-1),Power(FSymbol,Times(e,Plus(c,Times(d,x)))))))),And(And(FreeQ(List(FSymbol,GSymbol,$s("H"),a,b,c,d,e,f,g,h,r,s,t,n),x),Not(RationalQ(FullSimplify(Times(Plus(Times(g,h,Log(GSymbol)),Times(s,t,Log($s("H")))),Power(Times(d,e,Log(FSymbol)),-1)))))),Not(IntegerQ(n))))),
ISetDelayed(Int(Times(Power(G_,Times(h_DEFAULT,u_)),Power($p("H"),Times(t_DEFAULT,w_)),Power(Plus(a_,Times(b_DEFAULT,Power(F_,Times(e_DEFAULT,v_)))),n_)),x_Symbol),
    Condition(Int(Times(Power(GSymbol,Times(h,ExpandToSum(u,x))),Power($s("H"),Times(t,ExpandToSum(w,x))),Power(Plus(a,Times(b,Power(FSymbol,Times(e,ExpandToSum(v,x))))),n)),x),And(And(FreeQ(List(FSymbol,GSymbol,$s("H"),a,b,e,h,t,n),x),LinearQ(List(u,v,w),x)),Not(LinearMatchQ(List(u,v,w),x))))),
ISetDelayed(Int(Times(Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_)))),Power(Plus(Times(b_DEFAULT,Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_))))),Times(a_DEFAULT,Power(x_,n_DEFAULT))),p_DEFAULT)),x_Symbol),
    Condition(Plus(Times(Power(Plus(Times(a,Power(x,n)),Times(b,Power(FSymbol,Times(e,Plus(c,Times(d,x)))))),Plus(p,C1)),Power(Times(b,d,e,Plus(p,C1),Log(FSymbol)),-1)),Times(CN1,a,n,Power(Times(b,d,e,Log(FSymbol)),-1),Int(Times(Power(x,Plus(n,Negate(C1))),Power(Plus(Times(a,Power(x,n)),Times(b,Power(FSymbol,Times(e,Plus(c,Times(d,x)))))),p)),x))),And(FreeQ(List(FSymbol,a,b,c,d,e,n,p),x),NonzeroQ(Plus(p,C1))))),
ISetDelayed(Int(Times(Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_)))),Power(x_,m_DEFAULT),Power(Plus(Times(b_DEFAULT,Power(F_,Times(e_DEFAULT,Plus(c_DEFAULT,Times(d_DEFAULT,x_))))),Times(a_DEFAULT,Power(x_,n_DEFAULT))),p_DEFAULT)),x_Symbol),
    Condition(Plus(Times(Power(x,m),Power(Plus(Times(a,Power(x,n)),Times(b,Power(FSymbol,Times(e,Plus(c,Times(d,x)))))),Plus(p,C1)),Power(Times(b,d,e,Plus(p,C1),Log(FSymbol)),-1)),Times(CN1,a,n,Power(Times(b,d,e,Log(FSymbol)),-1),Int(Times(Power(x,Plus(m,n,Negate(C1))),Power(Plus(Times(a,Power(x,n)),Times(b,Power(FSymbol,Times(e,Plus(c,Times(d,x)))))),p)),x)),Times(CN1,m,Power(Times(b,d,e,Plus(p,C1),Log(FSymbol)),-1),Int(Times(Power(x,Plus(m,Negate(C1))),Power(Plus(Times(a,Power(x,n)),Times(b,Power(FSymbol,Times(e,Plus(c,Times(d,x)))))),Plus(p,C1))),x))),And(FreeQ(List(FSymbol,a,b,c,d,e,m,n,p),x),NonzeroQ(Plus(p,C1))))),
ISetDelayed(Int(Times(Power(x_,m_DEFAULT),Power(Plus(a_DEFAULT,Times(b_DEFAULT,Power(F_,u_)),Times(c_DEFAULT,Power(F_,v_))),-1)),x_Symbol),
    Condition(Module(List(Set(q,Rt(Plus(Sqr(b),Times(CN1,C4,a,c)),C2))),Condition(Plus(Times(C2,c,Power(q,-1),Int(Times(Power(x,m),Power(Plus(b,Negate(q),Times(C2,c,Power(FSymbol,u))),-1)),x)),Times(CN1,C2,c,Power(q,-1),Int(Times(Power(x,m),Power(Plus(b,q,Times(C2,c,Power(FSymbol,u))),-1)),x))),NonzeroQ(q))),And(And(And(FreeQ(List(FSymbol,a,b,c),x),ZeroQ(Plus(v,Times(CN1,C2,u)))),LinearQ(u,x)),PositiveIntegerQ(m)))),
ISetDelayed(Int(Times(Power(F_,u_),Power(x_,m_DEFAULT),Power(Plus(a_DEFAULT,Times(b_DEFAULT,Power(F_,u_)),Times(c_DEFAULT,Power(F_,v_))),-1)),x_Symbol),
    Condition(Module(List(Set(q,Rt(Plus(Sqr(b),Times(CN1,C4,a,c)),C2))),Condition(Plus(Times(Plus(C1,Times(CN1,b,Power(q,-1))),Int(Times(Power(x,m),Power(Plus(b,Negate(q),Times(C2,c,Power(FSymbol,u))),-1)),x)),Times(Plus(C1,Times(b,Power(q,-1))),Int(Times(Power(x,m),Power(Plus(b,q,Times(C2,c,Power(FSymbol,u))),-1)),x))),NonzeroQ(q))),And(And(And(FreeQ(List(FSymbol,a,b,c),x),ZeroQ(Plus(v,Times(CN1,C2,u)))),LinearQ(u,x)),PositiveIntegerQ(m)))),
ISetDelayed(Int(Times(Power(x_,m_DEFAULT),Power(Plus(Times(b_DEFAULT,Power(F_,v_)),Times(a_DEFAULT,Power(F_,Plus(c_DEFAULT,Times(d_DEFAULT,x_))))),-1)),x_Symbol),
    Condition(Module(List(Set(u,Block(List(Set($s("§showsteps"),False),Set($s("§stepcounter"),Null)),Int(Power(Plus(Times(a,Power(FSymbol,Plus(c,Times(d,x)))),Times(b,Power(FSymbol,v))),-1),x)))),Plus(Times(Power(x,m),u),Times(CN1,m,Int(Times(Power(x,Plus(m,Negate(C1))),u),x)))),And(And(And(FreeQ(List(FSymbol,a,b,c,d),x),ZeroQ(Plus(c,Times(d,x),v))),RationalQ(m)),Greater(m,C0)))),
ISetDelayed(Int(Times(u_,Power(Plus(a_,Times(b_DEFAULT,Power(F_,v_)),Times(c_DEFAULT,Power(F_,w_))),-1)),x_Symbol),
    Condition(Int(Times(u,Power(FSymbol,v),Power(Plus(c,Times(a,Power(FSymbol,v)),Times(b,Power(FSymbol,Times(C2,v)))),-1)),x),And(And(And(And(FreeQ(List(FSymbol,a,b,c),x),LinearQ(v,x)),LinearQ(w,x)),ZeroQ(Plus(v,w))),If(RationalQ(Coefficient(v,x,C1)),Greater(Coefficient(v,x,C1),C0),Less(LeafCount(v),LeafCount(w)))))),
ISetDelayed(Int(Times(Power(F_,Times(g_DEFAULT,Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),n_DEFAULT))),Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),-1)),x_Symbol),
    Condition(Int(ExpandIntegrand(Power(FSymbol,Times(g,Power(Plus(d,Times(e,x)),n))),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),-1),x),x),FreeQ(List(FSymbol,a,b,c,d,e,g,n),x))),
ISetDelayed(Int(Times(Power(F_,Times(g_DEFAULT,Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),n_DEFAULT))),Power(Plus(a_,Times(c_DEFAULT,Sqr(x_))),-1)),x_Symbol),
    Condition(Int(ExpandIntegrand(Power(FSymbol,Times(g,Power(Plus(d,Times(e,x)),n))),Power(Plus(a,Times(c,Sqr(x))),-1),x),x),FreeQ(List(FSymbol,a,c,d,e,g,n),x))),
ISetDelayed(Int(Times(Power(F_,Times(g_DEFAULT,Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),n_DEFAULT))),Power(u_,m_DEFAULT),Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_,Sqr(x_))),-1)),x_Symbol),
    Condition(Int(ExpandIntegrand(Power(FSymbol,Times(g,Power(Plus(d,Times(e,x)),n))),Times(Power(u,m),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),-1)),x),x),And(And(FreeQ(List(FSymbol,a,b,c,d,e,g,n),x),PolynomialQ(u,x)),IntegerQ(m)))),
ISetDelayed(Int(Times(Power(F_,Times(g_DEFAULT,Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),n_DEFAULT))),Power(u_,m_DEFAULT),Power(Plus(a_,Times(c_,Sqr(x_))),-1)),x_Symbol),
    Condition(Int(ExpandIntegrand(Power(FSymbol,Times(g,Power(Plus(d,Times(e,x)),n))),Times(Power(u,m),Power(Plus(a,Times(c,Sqr(x))),-1)),x),x),And(And(FreeQ(List(FSymbol,a,c,d,e,g,n),x),PolynomialQ(u,x)),IntegerQ(m)))),
ISetDelayed(Int(Power(F_,Times(Plus(a_DEFAULT,Times(b_DEFAULT,Power(x_,4))),Power(x_,-2))),x_Symbol),
    Condition(Plus(Times(Sqrt(Pi),Power(E,Times(C2,Sqrt(Times(CN1,a,Log(FSymbol))),Sqrt(Times(CN1,b,Log(FSymbol))))),Erf(Times(Plus(Sqrt(Times(CN1,a,Log(FSymbol))),Times(Sqrt(Times(CN1,b,Log(FSymbol))),Sqr(x))),Power(x,-1))),Power(Times(C4,Sqrt(Times(CN1,b,Log(FSymbol)))),-1)),Times(CN1,Sqrt(Pi),Power(E,Times(CN2,Sqrt(Times(CN1,a,Log(FSymbol))),Sqrt(Times(CN1,b,Log(FSymbol))))),Erf(Times(Plus(Sqrt(Times(CN1,a,Log(FSymbol))),Times(CN1,Sqrt(Times(CN1,b,Log(FSymbol))),Sqr(x))),Power(x,-1))),Power(Times(C4,Sqrt(Times(CN1,b,Log(FSymbol)))),-1))),FreeQ(List(FSymbol,a,b),x))),
ISetDelayed(Int(Times(Power(x_,m_DEFAULT),Power(Plus(Power(E,x_),Power(x_,m_DEFAULT)),n_)),x_Symbol),
    Condition(Plus(Times(CN1,Power(Plus(Power(E,x),Power(x,m)),Plus(n,C1)),Power(Plus(n,C1),-1)),Int(Power(Plus(Power(E,x),Power(x,m)),Plus(n,C1)),x),Times(m,Int(Times(Power(x,Plus(m,Negate(C1))),Power(Plus(Power(E,x),Power(x,m)),n)),x))),And(And(And(RationalQ(m,n),Greater(m,C0)),Less(n,C0)),Unequal(n,CN1)))),
ISetDelayed(Int(Log(Plus(d_,Times(e_DEFAULT,Power(Power(F_,Times(c_DEFAULT,Plus(a_DEFAULT,Times(b_DEFAULT,x_)))),n_DEFAULT)))),x_Symbol),
    Condition(Plus(Times(x,Log(Plus(d,Times(e,Power(Power(FSymbol,Times(c,Plus(a,Times(b,x)))),n))))),Times(CN1,x,Log(Plus(C1,Times(e,Power(d,-1),Power(Power(FSymbol,Times(c,Plus(a,Times(b,x)))),n))))),Int(Log(Plus(C1,Times(e,Power(d,-1),Power(Power(FSymbol,Times(c,Plus(a,Times(b,x)))),n)))),x)),And(FreeQ(List(FSymbol,a,b,c,d,e,n),x),NonzeroQ(Plus(d,Negate(C1)))))),
ISetDelayed(Int(Times(u_DEFAULT,Power(Times(a_DEFAULT,Power(F_,v_)),n_)),x_Symbol),
    Condition(Times(Power(Times(a,Power(FSymbol,v)),n),Power(Power(FSymbol,Times(n,v)),-1),Int(Times(u,Power(FSymbol,Times(n,v))),x)),And(FreeQ(List(FSymbol,a,n),x),Not(IntegerQ(n))))),
ISetDelayed(Int(u_,x_Symbol),
    Condition(Module(List(Set(v,FunctionOfExponential(u,x))),Times(v,Power(D(v,x),-1),Subst(Int(Times(FunctionOfExponentialFunction(u,x),Power(x,-1)),x),x,v))),FunctionOfExponentialQ(u,x))),
ISetDelayed(Int(Times(u_DEFAULT,Power(Plus(Times(a_DEFAULT,Power(F_,v_)),Times(b_DEFAULT,Power(F_,w_))),n_)),x_Symbol),
    Condition(Int(Times(u,Power(FSymbol,Times(n,v)),Power(Plus(a,Times(b,Power(FSymbol,ExpandToSum(Plus(w,Negate(v)),x)))),n)),x),And(And(FreeQ(List(FSymbol,a,b,n),x),NegativeIntegerQ(n)),LinearQ(List(v,w),x)))),
ISetDelayed(Int(Times(u_DEFAULT,Power(Plus(Times(a_DEFAULT,Power(F_,v_)),Times(b_DEFAULT,Power(G_,w_))),n_)),x_Symbol),
    Condition(Int(Times(u,Power(FSymbol,Times(n,v)),Power(Plus(a,Times(b,Power(E,ExpandToSum(Plus(Times(Log(GSymbol),w),Times(CN1,Log(FSymbol),v)),x)))),n)),x),And(And(FreeQ(List(FSymbol,GSymbol,a,b,n),x),NegativeIntegerQ(n)),LinearQ(List(v,w),x)))),
ISetDelayed(Int(Times(u_DEFAULT,Power(Plus(Times(a_DEFAULT,Power(F_,v_)),Times(b_DEFAULT,Power(F_,w_))),n_)),x_Symbol),
    Condition(Times(Power(Plus(Times(a,Power(FSymbol,v)),Times(b,Power(FSymbol,w))),n),Power(Times(Power(FSymbol,Times(n,v)),Power(Plus(a,Times(b,Power(FSymbol,ExpandToSum(Plus(w,Negate(v)),x)))),n)),-1),Int(Times(u,Power(FSymbol,Times(n,v)),Power(Plus(a,Times(b,Power(FSymbol,ExpandToSum(Plus(w,Negate(v)),x)))),n)),x)),And(And(FreeQ(List(FSymbol,a,b,n),x),Not(IntegerQ(n))),LinearQ(List(v,w),x)))),
ISetDelayed(Int(Times(u_DEFAULT,Power(Plus(Times(a_DEFAULT,Power(F_,v_)),Times(b_DEFAULT,Power(G_,w_))),n_)),x_Symbol),
    Condition(Times(Power(Plus(Times(a,Power(FSymbol,v)),Times(b,Power(GSymbol,w))),n),Power(Times(Power(FSymbol,Times(n,v)),Power(Plus(a,Times(b,Power(E,ExpandToSum(Plus(Times(Log(GSymbol),w),Times(CN1,Log(FSymbol),v)),x)))),n)),-1),Int(Times(u,Power(FSymbol,Times(n,v)),Power(Plus(a,Times(b,Power(E,ExpandToSum(Plus(Times(Log(GSymbol),w),Times(CN1,Log(FSymbol),v)),x)))),n)),x)),And(And(FreeQ(List(FSymbol,GSymbol,a,b,n),x),Not(IntegerQ(n))),LinearQ(List(v,w),x)))),
ISetDelayed(Int(Times(u_DEFAULT,Power(F_,v_),Power(G_,w_)),x_Symbol),
    Condition(Int(Times(u,NormalizeIntegrand(Power(E,Plus(Times(v,Log(FSymbol)),Times(w,Log(GSymbol)))),x)),x),And(FreeQ(List(FSymbol,GSymbol),x),Or(BinomialQ(Plus(v,w),x),And(PolynomialQ(Plus(v,w),x),LessEqual(Exponent(Plus(v,w),x),C2)))))),
ISetDelayed(Int(Times(y_DEFAULT,Plus(v_,w_),Power(F_,u_)),x_Symbol),
    Condition(Module(List(Set(z,Times(v,y,Power(Times(Log(FSymbol),D(u,x)),-1)))),Condition(Times(Power(FSymbol,u),z),ZeroQ(Plus(D(z,x),Times(CN1,w,y))))),FreeQ(FSymbol,x))),
ISetDelayed(Int(Times(w_,Power(F_,u_),Power(v_,n_DEFAULT)),x_Symbol),
    Condition(Module(List(Set(z,Plus(Times(Log(FSymbol),v,D(u,x)),Times(Plus(n,C1),D(v,x))))),Condition(Times(Coefficient(w,x,Exponent(w,x)),Power(Coefficient(z,x,Exponent(z,x)),-1),Power(FSymbol,u),Power(v,Plus(n,C1))),And(Equal(Exponent(w,x),Exponent(z,x)),ZeroQ(Plus(Times(w,Coefficient(z,x,Exponent(z,x))),Times(CN1,z,Coefficient(w,x,Exponent(w,x)))))))),And(And(And(FreeQ(List(FSymbol,n),x),PolynomialQ(u,x)),PolynomialQ(v,x)),PolynomialQ(w,x))))
  );
}
